C Exercises: Find any number between 1 and n that can be expressed as the sum of two cubes

C Numbers: Exercise-31 with Solution

Write a program in C to find any number between 1 and n that can be expressed as the sum of two cubes in two (or more) different ways.

Sample Solution:

C Code:

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

int main()
{
    int a, b, c, d, n; // Variables to represent four numbers and a limit 'n'
    double result; // Variable to store the result

    printf("\n\n Find the numbers between a range that can be expressed as the sum of two cubes:\n");
    printf("------------------------------------------------------------------------------------\n");
    printf(" The numbers in the above range are: \n");

    n = 100000; // Setting the limit 'n' for the range of numbers to be checked

    // Loop to find numbers in the range that can be expressed as the sum of two cubes
    for (a = 1; a <= n; a++)
    {
        int a3 = a * a * a; // Calculating the cube of 'a'
        if (a3 > n)
            break;

        for (b = a; b <= n; b++)
        {
            int b3 = b * b * b; // Calculating the cube of 'b'
            if (a3 + b3 > n)
                break;

            for (c = a + 1; c <= n; c++)
            {
                int c3 = c * c * c; // Calculating the cube of 'c'
                if (c3 > a3 + b3)
                    break;

                for (d = c; d <= n; d++)
                {
                    int d3 = d * d * d; // Calculating the cube of 'd'
                    if (c3 + d3 > a3 + b3)
                        break;

                    if (c3 + d3 == a3 + b3)
                    {
                        // Printing numbers that satisfy the condition: a^3 + b^3 = c^3 + d^3
                        printf(" %d = ", (a3 + b3));
                        printf("%d^3 + %d^3 = ", a, b);
                        printf("%d^3 + %d^3", c, d);
                        printf("\n");
                    }
                }
            }
        }
    }
    return 0;
}

Sample Output:

 The numbers in the above range are:                                                                          
 1729 = 1^3 + 12^3 = 9^3 + 10^3                                                                               
 4104 = 2^3 + 16^3 = 9^3 + 15^3                                                                               
 13832 = 2^3 + 24^3 = 18^3 + 20^3                                                                             
 39312 = 2^3 + 34^3 = 15^3 + 33^3                                                                             
 46683 = 3^3 + 36^3 = 27^3 + 30^3                                                                             
 32832 = 4^3 + 32^3 = 18^3 + 30^3                                                                             
 40033 = 9^3 + 34^3 = 16^3 + 33^3                                                                             
 20683 = 10^3 + 27^3 = 19^3 + 24^3                                                                            
 65728 = 12^3 + 40^3 = 31^3 + 33^3                                                                            
 64232 = 17^3 + 39^3 = 26^3 + 36^3 

Visual Presentation:

Flowchart:

C Programming Code Editor:

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